ADDITION: Add up all the ingredients using that common denominator, Find equivalent fractions , then add. Show all work. *
To add fractions with different denominators, you need to find a common denominator. Here's the step-by-step process:
1. Find a common denominator: Look for the least common multiple (LCM) of all the denominators.
2. Convert fractions to equivalent fractions with the common denominator: For each fraction, multiply both the numerator and the denominator by a factor such that the denominator becomes the common denominator.
3. Add the fractions: Once all the fractions have a common denominator, simply add the numerators together and keep the common denominator unchanged.
4. Simplify the fraction (if necessary): If possible, simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and denominator, then dividing both by it.
Now, let's apply this method to an example:
Suppose we want to add the fractions 1/3, 1/4, and 1/6.
Step 1: Finding the common denominator.
The least common multiple (LCM) of 3, 4, and 6 is 12.
Step 2: Converting fractions to equivalent fractions.
To convert 1/3 to a fraction with a denominator of 12, multiply both the numerator and denominator by 4 to get 4/12.
To convert 1/4 to a fraction with a denominator of 12, multiply both the numerator and denominator by 3 to get 3/12.
To convert 1/6 to a fraction with a denominator of 12, multiply both the numerator and denominator by 2 to get 2/12.
So, the fractions become 4/12, 3/12, and 2/12.
Step 3: Adding the fractions.
Add the numerators (4 + 3 + 2) to get 9. The common denominator remains 12.
Therefore, the sum of the fractions is 9/12.
Step 4: Simplifying the fraction (if necessary).
The greatest common divisor (GCD) of 9 and 12 is 3. Divide both the numerator and denominator by 3 to simplify the fraction.
The simplified fraction is 3/4.
So, 1/3 + 1/4 + 1/6 = 3/4.
Note: The above explanation provides a general method for adding fractions with different denominators. Please provide specific fractions if you want a detailed example.